Customer Reviews

Elements of Information Theory 2nd Edition (Wiley Series in Telecommunications and Signal Processing)

5 star:		(7)
4 star:		(1)
3 star:		(3)
2 star:		(2)
1 star:		(0)

 

 

I am writing this review in response to some confusion and unfairness I see in other reviews. Cover and Thomas have written a unique and ambitious introduction to a fascinating and complex subject; their book must be judged fairly and not compared to other books that have entirely different goals.

Claude Shannon provided a working definition of "information" in his seminal 1948 paper, A Mathematical Theory of Communication. Shannon's interest in that and subsequent papers was the attainment of reliable communication in noisy channels. The definition of information that Shannon gave was perfectly fitted to this task; indeed, it is easily shown that in the context studied by Shannon, the only meaningful measure of information content that will apply to random variables with known distribution must be (up to a multiplicative constant) of the now-familiar form h(p) = log(1/p).

However, Shannon freely admitted that his definition of information was limited in scope and was never envisioned as being universal. Shannon deliberately avoided the "murkier" aspects of human communication in framing his definitions; problematic themes such as knowledge, semantics, motivations and intentions of the sender and/or receiver, etc., were avoided altogether.

For several decades, Information Theory continued to exist as a subset of the theory of reliable communication. Some classical and highly regarded texts on the subject are Gallager, Ash, Viterbi and Omura, and McEliece. For those whose interest in Information Theory is motivated largely by questions from the field of digital communications, these texts remain unrivalled standards; Gallager, in particular, is so highly regarded by those who learned from it that it is still described as superior to many of its more recent, up-to-date successors.

In recent decades, Information Theory has been applied to problems from across a wide array of academic disciplines. Physicists have been forced to clarify the extent to which information is conserved in order to completely understand black hole dynamics; biologists have found extensive use of Information Theoretic concepts in understanding the human genome; computer scientists have applied Information Theory to complex issues in computational vs. descriptive complexity (the Mandelbrot set, which has been called the most complex set in all of mathematics, is actually extremely simple from the point of view of Kolmogorov complexity); and John von Neumann's brilliant creation, game theory, which has been called "a universal language for the unification of the behavioral sciences," is intimately coupled to Information Theory, perhaps in ways that have not yet been fully appreciated or explored.

Cover and Thomas' book "Elements of Information Theory" is written for the reader who is interested in these eclectic and exciting applications of Information Theory. This book does NOT treat Information Theory as a subset of reliable communication theory; therefore, the book is NOT written as a competitor for Gallager's classic text. Critics who ask
for a more thorough treatment of rate distortion theory or convolutional codes are criticizing the authors for failing to include topics that are not even central to their goals for the text!

A very selective list of some of the more interesting topics that Cover and Thomas study includes: (1) the Asymptotic Equipartition Property and its consequences for data compression; (2) Information Theory and gambling; (3) Kolmogorov complexity and Chaitin's Omega; (4) Information Theory and statistics; and (5) Information Theory and the stock market. Item (4) on this list is only briefly introduced in Cover and Thomas's book, and appropriately so; however, readers who wish to pursue the fascinating subject of Fischer Information further should consider B. Roy Frieden's book Physics from Fisher Information: A Unification. Frieden identifies a principle of "extreme physical information" as a unifying theme across all of physics, deriving such classic equations as the Klein-Gordon equation, Maxwell's equations, and Einstein's field equations for general relativity from this information-theoretic principle.

This last point is quite typical of Cover and Thomas's book. I participated in a faculty seminar on Information Thoery at my university a few years ago, in which we studied Cover and Thomas as our primary source. We were a diverse group, drawn from five different academic disciplines, and we all found that Cover and Thomas repeatedly introduced us to exciting and unexpected applications of Information Theory, always sending us to the journals for further, more in-depth study.

Cover and Thomas' book has become an established favorite in university courses on information theory. In truth, the book has few competitors. Interested readers looking for additional references might also consider David MacKay's book Information Theory, Inference, and Learning Algorithms, which has as a primary goal the use of information theory in the study of Neural Networks and learning algorithms. George Klir's book Uncertainty and Information considers many alternative measures of information/uncertainty, moving far beyond the classical log(1/p) measure of Shannon and the context in which it arose. Jan Kahre's iconoclastic book The Mathematical Theory of Information is an intriguing alternative in which the so-called Law of Diminishing Information is elevated to primary axiomatic status in deriving measures of information content. I alluded to some of the "murkier" issues of human communication earlier; readers who wish to study some of those issues will find Yehoshua Bar-Hillel's book Language and Information a useful source.

In conclusion, I highly recommend Cover and Thomas' book on Information Theory. It is currently unrivalled as a rigorous introduction to applications of Information Theory across the curriculum. As a person who used to work in the general area of signals analysis, I resist all comparisons of Cover and Thomas' book with the classic text of Gallager; the books have vastly different goals and very little overlap.

The preface of this book says, 'This is intended to be a simple and accessible book on information theory.' That's true, but it is aimed at the senior year or early graduate level where a theoretical background is needed for computer science, communications engineering, applied mathematics or similar fields. The mathematical nature of the book says that the student should at least have a background through calculus and a couple of upper level courses in statistics/probability. After all, Information Theory is generally considered to be a branch of applied mathematics.

On the whole, the writing style of the book (other than the equasions) is rather light and entertaining. For instance his discussion on the similarities between gambling and data compression brings a rather complex notion down something we can identify - that's before he gets into the math of course.

One complaint about the first edition of the book was that it didn't have enough problems for the student. This has been solved by the addition of a couple of hundred additional problems. There is also a dedicated web site for this book with more material, including solutions to selected problems.

Elements of Information Theory was the book I used in graduate school. It takes a topical approach to the subject from standard topics like source and channel coding, esoteric concepts like Kolmogorov complexity, to applied topics like how to get rich by applying Information theory to horse racing and the stock market. Overall I thought it was a good book. It is well written and exposes the grandure of subject. However what it provides in bredth it takes away in depth. Several topics, including fundemental ones like entropy, while well illustrated are not at all motivated - they are just given as definitions. In this I feel Galleghers book is superior. Also there is a real dearth of problems, its unusual to do all the problems in a book and feel you have not done enough to understand the material. Many a time I found myself scouring the web for more problems to augment the ones provided. So if you are looking for a broad view of the subject of information theory, this is the book to buy. If you are looking for a deeper understanding of the fundamental topics get Gallegher.

They often use (or overload) notation without first defining it, leaving the reader to guess at what they mean. When this occurred within the text I was usually able to figure it out by deducing definitions based on the results obtained with them, but it added unnecessary difficulty to reading the text and negated any illustrative value the example would have provided. Worse, they also did this in the problems. I never once had to obtain help solving the problems, but frequently had to obtain clarification of what the problems were asking.

The proofs often skip steps and omit justifications for most steps, including keystone steps of the proof. I would not have been able to follow many of the proofs had it not been for additional details provided in lecture. The preface is clear that this is intentional.

Finally, despite being a second edition, there are a fair number of typos, especially in the problems.

While there is always a trade-off between rigor and accessibility when writing a textbook, each of the above failings cause the book to be both less rigorous and less approachable, greatly increasing the frustration of trying to learn the material.

I have not read any other information theory texts, so I can't compare against those, but compared to other technical books I have read during my undergrad and graduate studies, this was one of the least helpful.

I give this book five stars for its outstanding clarity, thoroughness, and choice of topics. The writing is excellent, and most topics are easy to understand, although I have a few isolated quibbles about how certain topics are presented.

I feel like the chapters on continuous channels are much tougher to understand and less intuitive than the chapters on discrete channels.

The exercises are very useful, but in my opinion, a bit too easy. There are lots of exercises at the end of each chapter, but there are very few that require deep thinking or creative insight. Most of the exercises are fairly routine. I think a few more involved ones would be welcome.

The one thing that is most lacking in this book are examples. The bulk of the text is made up in exposition of new ideas and proofs of theorems. While the exercises give lots of examples, I still feel that something is missing--especially in the chapters on continuous channels.

As a supplement, I would recommend "Information Theory, Inference, and Learning Algorithms" by MacKay. The two books are very different from each other and have less overlap than one might expect; I think everyone would do well to study both books. That book is much more suitable for self-study, has more concrete examples, and is in my opinion more fun and interesting (which says a lot, because this book is itself quite fun and interesting). It also has some more involved exercises. Also, it covers coding theory in more depth than this book (something that one might not realize from its name), and it integrates a Bayesian perspective into things more deeply.

The book is nice! It goes through the information theory contents with significant and easy-to-handle examples. Read it!

This textbook was used in a class I took in information theory for upper-division undergraduates and first-year graduate students. The book relies on a solid understanding of probability and a reasonable level of mathematical maturity. I took the class after two years of probability and a year of analysis, and found the proofs very easy to follow. The problems ranged from easy to slightly involved; all helped illustrate subtleties the reader might otherwise miss. The book doesn't use any particularly advanced mathematics, but people who aren't as familiar with proofs may struggle with the seemingly endless number of small "tricks" used. Some exposure to analysis helps here.

Very good book with some minor issues. The authors do a great job of making most of the material accessible to a person with an understanding of basic probability. In my humble opinion, the chapters on Gaussian Channel (Ch9) and Network Information Theory (Ch15) need more exposition. Other chapters are very well explained. Occasionally deep statements are made without much explanation and amplification. It is upto the reader to figure out explanations for these statements. Some of the problems are repeated. Most of the problems are easy and as another reviewer pointed out, the book might benefit with the addition of some more thought provoking problems. However a great book for learning information theory.

This book presents the subject Information Theory in a simple way, therefore, even the deeper concepts and hard subjects could be understood ! But the problems are not so easy. To solve them, the reader shall have experience in the area.
The summaries in the final of each chapter come out as a great feature to the new students in this area.

To finish: A Great Book !

Believe me, I have read many many textbooks. Not one is like this book. The problem is that the authors don't explain, to an extent where terms are not clearly defined. I have to frequently stop and GUESS what the authors mean by the symbols and terms, and writing something in that particular way. The flow of understanding is constantly stopped by these intensionally introduced hurdles. I say intensional because from the preface of the book I see that the authors are pretty proud of that.

I think I am already quite good at guessing what the authors of other books occasionally skip. But this one really annoys me. I think it is really a waste of time to have to guess something that is just basic definition.